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parallel paths being equivalent to that of a phase-lag network. The leaky integrator
path leads to a signal proportional to the angle through which the helicopter has been
disturbed; this initially provides an input to the swash plate that counteracts the
angular disturbance. In the longer term, the input decays or ‘leaks away’, so that if
the helicopter does not respond to the corrective action, or the pilot holds the new
attitude, then the final angular position becomes the new equilibrium state.
(b) ASE (automatic stabilisation equipment)
The ASE is designed to control a desired attitude, e.g. pitch or roll. The attitude
angles are sensed from a gyro and these, and their rates which are found by
differentiation, are summed in appropriate proportions, together with signals from
the cyclic stick (control) position and the c.g. trim system. The latter centres the gyro
to a datum corresponding to successive new flight conditions. The signal from the
stick is used to cancel the gyro signal when the pilot demands a manoeuvre, otherwise
the attitude control would hold the original datum and oppose the manoeuvre demanded.
5.9 Control response
We now consider the behaviour of the helicopter in response to the pilot’s control
input and to vertical gusts. A detailed account of the motion following these disturbances
would be out of place here, and the discussion will be limited to those features of
helicopter response which are usually regarded as being the most important. These
are
(a) the normal acceleration in response to a cyclic pitch displacement,
(b) the normal acceleration in response to a vertical gust,
(c) the pitching and rolling response to cyclic pitch displacements.
Response to collective pitch changes will not be considered, since it is not normally
regarded as a ‘short-term’ control, although it may be possibly used in an autostabilisation
system.
Detailed knowledge of the control response is essential for determining the flying
qualities of a helicopter, and subsequent assessment of how these relate to the separately
identifiable tasks within a flying mission. An extensive treatment of the topic is
provided in Padfield3.
In order to proceed with this limited study of the control response, the force and
moment derivatives with respect to cyclic and collective pitch applications are now found.
180 Bramwell’s Helicopter Dynamics
5.9.1 The B1 control derivatives
The application of longitudinal cyclic pitch tilts the no-feathering axis in the longitudinal
plane and produces precisely the same effect as if the cyclic stick had been kept fixed
and the incidence of the helicopter had been reduced by the same amount, i.e.
ΔB1 = –Δα = –(1/μ)Δwˆ
or ∂
∂
∂
B1 ∂ w
= –μ ˆ
Thus
∂
∂
∂
∂
t
B
t
w
c
1
= –μ cˆ
(5.142)
∂
∂
∂
∂
h
B
h
w
c
1
D = –μ cDˆ
(5.143)
∂
∂
∂
∂
a
B
a
w
1
1
= –μ 1 ˆ (5.144)
the w derivatives being given by eqns 5.79 to 5.81.
In obtaining the force and moment derivatives we have to allow for the fact that
the no-feathering axis moves relative to the shaft when cyclic pitch is applied. Thus,
the X force must be written
X = – T sin αD – HD cos αD
= – T sin (αs + a1 – B1) – HD cos(αs + a1 – B1)
where αs is the incidence of the shaft (rotor hub axis)
Then
∂
∂
∂
∂
∂
∂
X
B
X
T
B
T
a
B B
1 1
D D
1
1
= = – sin – cos – 1 1 α α 
 
 
+ D cos + sin – 1
1
D D D
1
1
∂
∂
∂
∂
H
B
H
a
B
α α 
 
 
(5.145)
≈ 
 
 
– + 1 + –
1
D
1 D
1
∂
∂
∂
∂
∂
∂
T
B
T
a
w
H
B
α μ ˆ (5.146)
In non-dimensional form,
x
X
sA R
t
B
　
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本文鏈接地址：Bramwell’s Helicopter Dynamics(92)